4 citations · 4 across the 3 of their papers we have counts for
8 papers · 1 filter
The Classification of Graphs on vertices with Coinciding Zero Forcing number and Maximum Nullity
Wayne Barrett, Mark Hunnell, John Hutchens +1
We study the minimum rank of a (simple, undirected) graph, which is the minimum rank among all matrices in a space determined by the graph. We determine the exact set of graphs on…
Unicyclic graphs and the inertia of the distance squared matrix
Christian Howell, Mark Kempton, Kellon Sandall +1
A result of Bapat and Sivasubramanian gives the inertia of the distance squared matrix of a tree. We develop general tools on how pendant vertices and degree 2 vertices affect the…
Graphs with few trivial characteristic ideals
Carlos A. Alfaro, Michael D. Barrus, John Sinkovic +1
We give a characterization of the graphs with at most three trivial characteristic ideals. This implies the complete characterization of the regular graphs whose critical groups ha…
Characterizing cospectral vertices via isospectral reduction
Mark Kempton, John Sinkovic, Dallas Smith +1
Two emerging topics in graph theory are the study of cospectral vertices of a graph, and the study of isospectral reductions of graphs. In this paper, we prove a fundamental relati…
Spanning 2-Forests and Resistance Distance in 2-Connected Graphs
Wayne Barrett, Emily J. Evans, Amanda E. Francis +2
A spanning 2-forest separating vertices and of an undirected connected graph is a spanning forest with 2 components such that and are in distinct components. Aside…
Average mixing matrix of trees
Chris Godsil, Krystal Guo, John Sinkovic
We investigate the rank of the average mixing matrix of trees, with all eigenvalues distinct. The rank of the average mixing matrix of a tree on vertices with distinct eige…